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Solutions to Problems Related to Psychrometry

a) Air at 38 C db and 18 C wb is humidified adiabatically with steam. The steam supplied contains 20 percent moisture (quality of 0.80) at 101.3 kPa. If the air is humidified to 60 percent relative humidity, what is the dry bulb temperature of the humidified air? Assume sea level pressure.

(b) Air at 5 C db and 2 C wb is mixed with warm air at 38 C db and 25 C wb in the ratio of 2 kg cool air to 1 kga of warm air. (i) Compute the humidity ratio and enthalpy of the mixed air, and (ii) find the humidity ratio and enthalpy using psychrometric chart .

(a) An auditorium is to be maintained at 25 C dry bulb temperature and 50% relative humidity. The supply air enters the auditorium at 17 C. The sensible and latent heat loads are 150 kW and 61 kW, respectively. Determine the wet bulb temperature, relative humidity, and volume flow rate of the supply air.

(b) In a certain space to be air conditioned the sensible and latent heat loads are 20.60 kW and 6.78 kW, respectively. Outside air is at 33 C dry bulb and 24 C wet bulb temperatures. The space is to be maintained at 25 C with a relative humidity not exceeding 50%. All outside air is supplied with reheater. The conditioned air enters at 18°C. Determine (a) the refrigeration load required, (b) the capacity of the supply fan, and (c)
the heat supplied in the reheater

(a) An air conditioned auditorium with a capacity of 1000 persons is to be maintained at 24 C dry bulb temperature and 55% relative humidity. The sensible and latent heat loads are 115 kW and 42 kW, respectively. The conditioned air enters the auditorium at 17 C. For proper ventilation, 40% of the supply air is fresh air and the rest is recirculated air. Outside air is at 34 C and 50% relative humidity. Determine (a) the volume flow rate of
recirculated air, (b) the apparatus dew point, and (c) the refrigeration load.

(b) A meeting hall is to be maintained at 25 C db and 18 C wb. The barometric pressure is 101.3 kPa. The space has a load of 58.6 kW sensible and 58.6 kW latent. The temperature of the supply air cannot be lower than 18 C db. (a) How many kilograms per second of air must be supplied? (b) What is the required wet bulb temperature of the
supply air? (c) What is the sensible heat ratio?

Sol 1)

Given data,

Dry bulb temperature, = 38

Wet bulb temperature, = 18

Relative humidity after adiabatic humidification, = 60%

1. Plot the 1st state of the air at 38and 18. As the air is adiabatically humidified the line should be drawn from the 1st point to the relative humidity line of 60% and this line will be parallel to the wet bulb temperature. (In adiabatic humidification process the process line is parallel to wet bulb line)
2. Note the dry bulb temperature of the final state. The value of dry bulb temperature, = 23           (Answer)

Sol 2)

Given data,

Dry bulb temperature of cool air, = 5

Wet bulb temperature of cool air, = 2

Mass of cool air,  = 2kg

Dry bulb temperature of warm air, = 38

Wet bulb temperature of warm air, = 25

Mass of warm air,  = 1kg

By using formulae,

• Specific humidity(humidity ratio) of the mixture is given by,

=

=                                                                                                        (values   )

=

= 0.007kg/kg of dry air.                                    (Answer)

• Enthalpy of the mixture is given by,

h=

=

=

=34.33 kJ/kg of dry air.                         (Answer)

By using psychrometric chart,

Plot the two states on the psychrometric chart using the values of dry bulb temperature and the wet bulb temperature.

Join these two points and divide the line in the ratio 2:1

The value of relative humidity and the enthalpy at that point is the required solution.

Relative humidity (humidity ratio) = 0.0073kg/kg of dry air.          (Answer)

Enthalpy of the mixture = 34.35 kJ/kg of dry air.                                      (Answer)

Sol 3)

Given data,

Dry bulb temperature, = 25

Relative humidity,= 50%

Dry bulb temperature, = 17

We know that,

Room sensible heat factor (RSHF) =

=

= 0.710

First of all, mark room condition of air i.e. 25 and 50% relative humidity as point 1 on psychrometric chart.  Now mark the RSHF value (0.710) on sensible heat factor scale and mark it as point “a”. Now join the point “a” to the alignment circle (26 dry bulb temperature and 50% relative humidity). Now draw a line parallel to the above line from point 1 to point 2 till 17 dry bulb temperature. The wet bulb temperature is noted from point 2.

Relative humidity= 0.0086 kg/kg of dry air.                           (Answer)

Let volume flow rate be “v”.  We know that,

Room sensible heat (RSH) = 0.02044v ()

150   = 0.02044v (25-17)

150 = 0.02044v 8

v=

Sol 4)

As per the given data,

RSHF=

= 0.752

Using the psychrometric chart we have the value of

=

= 344.827 kg/min.

= 6.3 KW

Sol 5)

As per given data,

RSHF=

=0.732

Mass of air=

=

= 334.82 kg/min

Apparatus dew point= 11 (from psychrometric table)        (Answer)

Volume of recirculated air= 0.6334.82

Sol 6)

As per given data,

Sensible heat ratio =

Using the psychrometric chart,

We have